Localhost/example/wp-admin redirects to live site

Hello, and thanks in advance for any help.

I am attempting to make a local copy of a live WordPress site that I will be doing some editing on. I have successfully localized it to the point where I can navigate to localhost/mysite, but when I try to login to localhost/mysite/wp-admin, I get redirected to the live url. I have edited the home and siteurl files in wp_options to say localhost/mysite. I’ve looked through quite a few forums, and went through many of the suggested fixes, but nothing has worked thus far. Could someone please give me some pointers as to what I am missing?